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MHT CET202618 April 2026Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual

In ABC , if C = 3 , then the value of ^2 A + ^2 B + A B is...

Options

  1. A3 4
  2. B5 4
  3. C-3 4
  4. D-5 4

Correct answer

A. 3 4

Step-by-step solution

Given A + B + C = and C = 3 , we have A + B = 2 3 . The given expression is ^2 A + ^2 B + A B . Using the identity ^2 A + ^2 B = 1 + 2A + 2B 2 , we get: ^2 A + ^2 B = 1 + (A+B) (A-B) Also, using the product-to-sum formula: A B = (A+B) + (A-B) 2 Substituting these into the expression, we get: 1 + (A+B) (A-B) + (A+B) + (A-B) 2 Since A + B = 2 3 , we have (A+B) = ( 2 3 ) = - 1 2 . Substituting (A+B) = - 1 2 into the expression: 1 - 1 2 (A-B) + - 1 2 + (A-B) 2 = 1 - 1 2 (A-B) - 1 4 + 1 2 (A-B) = 1 - 1 4 = 3 4 Answer: 3

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